Rings of the Jovian Planets

Saturn has a famous ring system. Let's look at the rings. Other planets have rings too. What could they be? Why rings?
What would be wrong with just an unorganized swarm of particles?

Why not moons?

Davison E. Soper, Institute of Theoretical Science, University of Oregon, Eugene OR 97403 USA soper@bovine.uoregon.edu